1970 AHSME Problems/Problem 19
Problem
The sum of an infinite geometric series with common ratio such that is , and the sum of the squares of the terms of this series is . The first term of the series is
Solution
We know that the formula for the sum of an infinite geometric series is .
So we can apply this to the conditions given by the problem.
We have two equations:
We get
Since , , so plug this into the equation above and we get
Solution by
See also
1970 AHSC (Problems • Answer Key • Resources) | ||
Preceded by Problem 18 |
Followed by Problem 20 | |
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